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An element of a group is \emph{reversible} if it is conjugate to its owninverse, and it is \emph{strongly reversible} if it is conjugate to its inverseby an involution. A group element is strongly reversible if and only if it canbe expressed as a composite of two involutions. In this paper the reversiblemaps, the strongly reversible maps, and those maps that can be expressed as acomposite of involutions are determined in certain groups of piecewise linearhomeomorphisms of the real line.

Reversible maps and composites of involutions in groups of piecewise linear homeomorphisms of the real line